A Reciprocal Heuristic Model for Diffuse Scattering From Walls and Surfaces

Diffuse scattering (DS) of electromagnetic waves from natural and artificial surfaces has been extensively studied in various disciplines, including radio wave propagation, and several DS models based on different approaches have been proposed over the years, two of the most popular ones being Kirchhoff theory and the so-called effective roughness (ER) heuristic model. The latter, although less rigorous than the former, is more flexible and applicable to a wider range of real-world cases, including non-Gaussian surfaces, surfaces with electrically small correlation lengths and scattering from material inhomogeneities that are often present under the surface. Unfortunately, the ER model, with the exception of its Lambertian version, does not satisfy reciprocity, which is an important physical-soundness requirement for any propagation model. In the present work, without compromising its effectiveness and its simple and yet sound power-balance approach, we propose a reciprocal version of the ER model, which can be easily implemented and can replace the old version in ray-based propagation models. The new model is analyzed and compared with the old one and with other popular models. Once properly calibrated, it is shown to yield similar—if not better—performance with respect to the old one when checked versus measurements.